Diversity waves in collapse-driven population dynamics

Populations of species in ecosystems are constrained by the availability of resources within their environment. In effect this means that a growth of one population, needs to be balanced by the reduction in size of others. In neutral models of biodiversity all populations are assumed to change incrementally due to stochastic births and deaths of individuals. Here we propose and model another redistribution mechanism driven by abrupt collapses of the entire population of a single species freeing up resources for the remaining ones. This mechanism may be relevant for communities of bacteria, with strain-specific collapses caused e.g. by invading bacteriophages, or for other ecosystems where infectious diseases play an important role. The emergent property of the population dynamics in our system are cyclic "diversity waves" triggered by collapses of globally dominating populations. The population diversity in the environment peaks at the beginning of each wave and exponentially decreases afterwards. Population sizes in our system follow a bimodal distribution with the lower peak composed of the recently collapsed or the newly arrived species. In contrast to this, the upper peak of the distribution consists of the surviving species in the current diversity wave. The populations of the most abundant species in the upper peak exhibit a scale-free distribution with a nearly universal exponent of about 1.7. We show that our model is robust with respect to variations in dynamical rules including gradual redistribution of populations between subsequent collapses and variation in species' growth or collapse rates.